A376380 Products of 5 distinct primes that are sandwiched between twin prime numbers.
2310, 2730, 6090, 6270, 7590, 8970, 9282, 13398, 14322, 15330, 17490, 19470, 21318, 22110, 23370, 27690, 28182, 29670, 30090, 32190, 32370, 32718, 32802, 32970, 33330, 37590, 40530, 41610, 45318, 46830, 47058, 48678, 48990, 49170, 49530, 49938, 51198, 52710, 56238, 56910, 57270, 58110, 58170, 59010, 60762
Offset: 1
Keywords
Examples
2310 is in the sequence a term because 2310=2*3*5*7*11 is the product of five distinct primes and 2309, 2311 are a couple of twin primes. 2730 is in the sequence a term because 2730=2*3*5*7*13 is the product of five distinct primes and 2729, 2731 are a couple of twin primes.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
-
Maple
ispenta:= proc(n) local F; F:= ifactors(n)[2]; nops(F) = 5 and F[..,2] = [1$5] end proc: select(t -> isprime(t-1) and isprime(t+1) and ispenta(t), [seq(i,i=6 .. 10^5,12)]); # Robert Israel, Sep 24 2024
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Mathematica
Select[Range[6, 61000, 6], And @@ PrimeQ[# + {-1, 1}] && FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Sep 22 2024 *) -
PARI
list(lim)=my(v=List()); forprime(p=11,lim\210, my(P=lim\(6*p)); forprime(q=7,min(P\5,p-2), my(Q=P\q); forprime(r=5,min(Q,q-2), my(t=6*p*q*r); if(isprime(t+1) && isprime(t-1), listput(v,t))))); Set(v) \\ Charles R Greathouse IV, Sep 24 2024
Comments